Classical chaos and fluctuation-dissipation relations for nonlinear response

The classical nonlinear optical response is expressed in a form that closely resembles the fluctuation-dissipation theorem. The nth-order response is shown to depend on interferences among n closely lying trajectories. The relevant dynamical information on the vicinity of a given trajectory can be recast using the stability matrix related to the Lyapunov exponents. No such interference exists in the linear response, and the nonlinear response is consequently a much more sensitive probe for classical chaos. Sequences of multiple femtosecond pulses can be designed to directly probe the stability matrix.